Wednesday, 18 October 2017

FUNCTIONS 3


If f(x) = x4 - kx2 - 6x + 7 has a remainder of 22 when divided by x+2; find k.

solution

f(x) = x4 - kx2 - 6x + 7

x + 2 = 0

x = -2

f(x) = (-2)4 - k(-2)2 - 6(-2) + 7 = 22

16 - 4k + 12 + 7 = 22

16 - 4k + 19 = 22

16 + 19 = 22 + 4k

16 + 19 - 22=4k

35 - 22=4k

13 = 4k


k = 13/4    after dividing by 4 both sides.

hence k=13/4

TRY THIS......................


If f(x) = x4 - kx2 - 5x - 31 has a remainder of 18 when divided by x-2; find k.

PERCENTAGE PROFIT1


A man got a profit of 7400/= after selling an item. Find the buying price if the percentage profit was 5%.

Solution

%’ge profit = Profit   X  100    where B. P. represents Buying Price.
                        B.P

5% = 7400   X  100   
           B.P.

B.P. x 5% = 740,000   x B.P.  [multiplying by B.P. both sides]
                       B.P.

B.P. x 5 = 740,000   

B.P. x 51 =   740,000  148000 
  15                   51

B.P. = 148000
                      
Hence Buying Price was 148000/=
  
TRY THIS………………


A man got a profit of 27,500/= after selling an item. Find the buying price if the percentage profit was 20%.

VARIATION 2


x is directly proportional to y. x=24 while y=4. Find y when x is 60.

Solution

x y

x = ky

24 = k x 4

24 = 4k
4      4

k = 6
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 6, y= ? x = 60.


x = ky

60 = 6 x y

60 = 6y
6      6


y = 10.


TRY THIS…………….



x is directly proportional to y. x=48 while y=12. Find y when x is 70.

LOGARITHMS 3


If log 2= 0.3010; find the value of log 400,000 without using tables.

solution

= log 400,000

=log(100,000 x 4)


=log100,000 + log4


=log105 + log22


=5log10 + 2log2


=(5x1) + 2(0.3010)


=5– 2(0.3010)


=5 – 0.6020


=4.398


Hence log2500=3.398



TRY THIS……………



If log 2= 0.3010; find the value of log 80,000 without using tables.

Monday, 9 October 2017

EXPONENTIALS 3


Simplify the following by writing in power form:
(m55 x m15)/(m46 x m6)
  
Solution

= (m55 x m15)/(m46 x m6)

= m55+15
   m46+6 

= m70
    m52 

= m70-52

= m18


TRY THIS……………….


Simplify the following by writing in power form:

(a60 x a20)/(a46 x a14)


A. P. 1


The 1st term of arithmetic progression is 24 and the common difference is 40. Find the nth term

solution

A1=24, d= 40, n=?

An =A1 + (n-1) d

An=24 + (n-1)40

An=24 + 40n - 40

An=40n + 24 - 40

An=40n – 16

Hence the nth term is An=40n – 16  

TRY THIS………………….. 


The 1st term of arithmetic progression is 60 and the common difference is 122. Find the nth term.


AREAS 1


Area of a rectangle is 84 cm2. Find its perimeter if its width is 7cm.

Solution

First we find length

A =  l  x w

84 =  l  x 7

84 = 7l
7       7

12 =  l

Now length is 12cm.

We can find perimeter since we have both length and width.     

Let l = length and w = width;

P = 2(l + w)

   = 2(12 + 7)

   = 2 x 19

   = 38

Hence perimeter is 38 cm. 

TRY THIS………………….. 


Area of a rectangle is 100 cm2. Find its perimeter if its width is 4cm.

FUNCTIONS 2


If F(x) = 4x + 16; Find F-1(x).

Solution

HINT: F-1(x) means inverse.

PROCEDURE:
Make x the subject and then interchange x and y variables.

Let y=F(x)

So,  y= 4x + 16

y – 16 = 4x

y – 16  = 4x
   4          4

y – 16   = x
   4

x  =   y – 16     after rearranging
           4


F-1(x) = x – 16    after interchanging x and y variables.
                4

Hence, F-1(x) = x – 16     
                              4


TRY THIS………………   


If F(x) = 11x + 30; Find F-1(x).


BINARIES 1


If p*k = 4pk - p – 2k; find 3*2.

Solution

p*k = (4 x p x k) - p – (2xk)   [rewriting the given expression more clearly]


3*2 = (4 x 3 x 2) - 7 – (2x2)   [substituting 7 for p and 2 for k]


3*2 = 24 - 7 – 4


3*2 = 24 – 11   [since( -7-4) = -11]


3*2 = 13.


Hence   (3*2) = 13.


 TRY THIS........



If p*k = 5p + k – 5pk; find (-2*7).


SUM OF AP 2


The first term of an AP is 21 and the last term is 97. If the arithmetic progression consists of 20 terms, calculate the sum of all the terms. 

Solution

A1 = 21, n=20, An = 97

Sn = n(A1 + An)
       2

S20 = 20(21 + 97)
         2

S20 = 10 x 118

S20 = 1180


Hence the sum of all 20 terms is 1180.

TRYTHIS………………….



The sum of first 20 terms of an AP is 1380, and the last term is 97. Find the 1st term. 


EXPONENTIALS 2


Simplify the following by writing in power form:
w63
w40

Solution

= w63 - 40 

=w23

TRY THIS……………….

Simplify the following by writing in power form:
m55

m21 


VARIATION 1


x is inversely proportional to y. x=30 while y=5. Find y when x is 15.

Solution

x k
      y

x = k
      y

30 = k
        5

k = 30 x 5

k = 150

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 150, y= ?, x = 15.

x = k
      y

15 = 150
         y

y x 15 = 150  x  y   (multiply by y on both sides)
                y


15y = 150 10        dividing by 15 both sides
15      15

Hence y = 10  .


TRY THIS…………….



x is inversely proportional to y. x=80 while y=4. Find y when x is 40.

Saturday, 7 October 2017

SUM OF AP 1


The sum of first 20 terms of an AP is 1380, and the last term is 97. Find the 1st term. 

Solution

A1 = ?, n=20, An = 97, Sn =1380

Sn = n(A1 + An)
       2

1380 = 20(A1 + 97)
             2

1380 = 10(A1 + 97)

1380 = 10A1 + 970

1380 - 970= 10A1

410= 10A1

410= 10A1
10     10

41= A1

Hence 1st term is 41.


TRYTHIS……………



The sum of first 30 terms of an AP is 2475, and the last term is 105. Find the 1st term. 

EXPONENTIALS 1


Simplify the following by writing in power form:
(m55 x m5)/ m46 
   

Solution

= (m55 x m5)/ m46 

= m55+5
    m21 

= m60
    m21 

= m60-21

= m39


TRY THIS……………….


Simplify the following by writing in power form:
 (y65 x y51)/ y94 


LOGARITHMS 2


If Logax = 0.9, find Loga(x4)

Solution

= Loga(x4)

= 4Logax

= 4 x Logax

= 4 x 0.9

= 3.6


TRY THIS………..


If Logaw= 3.6, find Loga(w3)

Friday, 6 October 2017

LOGARITHMS 1


Evaluate Log1000000 +  log 0.001 -  log 0.00000001

Solution

= Log1000000 +  log 0.001 -  log 0.00000001

= Log106 +  log 10-3 – log 10-8

= 6Log10 + (-3 log 10) – (-8log 10)

= (6x1) + (-3x1) - (-8x1)

=6 + (-3) – (-8)

= 6 – 3 + 8

=11



Hence Log1000000 +  log 0.001-  log 0.00000001 = 11

POLYGONS 1


A regular polygon has 66 sides. Find the total degrees of that polygon.

Solution

n = 66

Total degrees = (n - 2)1800

                       = (66 – 2)1800

                       = 64 x 1800

                       = 115200

Total degrees = 115200


TRY THIS……………………….


A regular polygon has 33 sides. Find the total angles of that polygon.

FUNCTIONS 1


Find the maximum value of the quadratic equation:5-3t-8t2.

Solution

a=-8, b=-3, c=5

Maximum = 4ac-b2
                        4a

Maximum = (4 x -8 x 5) - (-3)2
                          4(-8)

Maximum = (-160)- 9
                        -32

Maximum= -169                         since (-160)- 9= -169
                    -32

Maximum = 169
                     32       

Hence maximum value is 169/32

TRY THIS………………………………..


Find the maximum value of the quadratic equation:6+10t-4t2.

Tuesday, 12 September 2017

RADICALS 1


Radicals are among the challenging concepts in maths.

With this video below you can learn one of them and reach to the solution.





See more Math Videos and ease your mathematics learning.



Saturday, 9 September 2017

ARITHMETICS 1


Evaluate 13 x 369 + 331 x 13.

Solution

= 13 x 369 + 331 x 13.

= 13 x (369 + 331)     factoring out the common number

= 13 x 700   

= 9100      [after multiplying 16 and 7 and adding two zeros on the answer]

Hence 13 x 369 + 331 x 13= 9100

TRY THIS………….



Evaluate 127 x 516 + 484 x 127.

SUM OF A GP 1


Find the sum of the 1st ten terms of the geometrical progression 2+6+18+54+…….

solution

G1 = 2, r=3, n=10

Sn = G1(rn-1)/r-1
               
S10 = 2(310-1)/3-1            

S10 = 12(310-1)/21
               
S10 = (310-1)

S10 = 59049 - 1

S10 = 59048

Hence the sum of the 1st seven terms is 19682.

TRY THIS………………



Find the sum of the 1st eight terms of the geometrical progression 3+9+27+81+…..

ALGEBRA 2


If │4x – 7 │= 15; Find  x

Solution

±(4x – 11 )= 17

4x -11= 15   OR   –(4x-11) = 15

4x – 11 = 15    OR   -4x+11=15

4x = 15 + 11    OR   -4x= 15-11

4x = 26     OR   -4x  =   4
4      4               -4        -4

x = 13/2  OR  x = -1


Hence x = 13/2  OR  x = -1


TRY THIS………………………. 


If │2x – 7 │= 25; Find  x